Gen 2 had Apricorns and different Pokeballs that are exclusive to Johto, could you transfer a Pokemon holding an Apricorn (if they can hold Apricorns) or a Heavy/Fast/Level/Lure/Moon/Friend/Love Ball into ORAS or X/Y
Pokemon cant hold apricorns as they are in Apricorn Boxes which are key items.
You can catch a female Pokemon with an Apricorn ball and transfer that over. Then when you breed the Pokemon all of its offsprings will be in the same ball.
Hope I helped